136 citations · 534 across the 27 of their papers we have counts for
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Multiple recurrence and convergence results associated to -actions
Vitaly Bergelson, Terence Tao, Tamar Ziegler
Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of . From this…
The shifted primes and the multidimensional Szemeredi and polynomial van der Waerden theorems
Vitaly Bergelson, Alexander Leibman, Tamar Ziegler
In this short note we establish new refinements of multidimensional Szemeredi and polynomial van der Waerden theorems along the shifted primes.
Multiple recurrence and convergence along the primes
Trevor D. Wooley, Tamar D. Ziegler
Let be a set of positive upper density. Suppose that are polynomials having zero constant terms. We show that the set $E\cap…
An inverse theorem for the uniformity seminorms associated with the action of
Vitaly Bergelson, Terence Tao, Tamar Ziegler
Let $\F$ a finite field. We show that the universal characteristic factor for the Gowers-Host-Kra uniformity seminorm $U^k(\X)$ for an ergodic action $(T_g)_{g \in \F^ω}$ of the in…
Nilfactors of R^m-actions and configurations in sets of positive upper density in R^m
Tamar Ziegler
We use ergodic theoretic tools to solve a classical problem in geometric Ramsey theory. Let E be a measurable subset of R^m, with positive upper density. Let V={0,v_1,...,v_k} be a…
Universal Characteristic Factors and Furstenberg Averages
Tamar Ziegler
Let X=(X^0,μ,T) be an ergodic measure preserving system. For a natural number k we consider the averages (*) 1/N \sum_{n=1}^N \prod_{j=1}^k f_j(T^{n a_j}x) where the functions f_j…
A Non Conventional Ergodic Theorem for a Nil-System
Tamar Ziegler
We prove a non conventional pointwise convergence theorem for a nilsystem, and give an explicit formula for the limit.